diff --git a/src/hooks/usePolygon.js b/src/hooks/usePolygon.js
index 328687fe..baefd30f 100644
--- a/src/hooks/usePolygon.js
+++ b/src/hooks/usePolygon.js
@@ -1,7 +1,7 @@
 import { ANGLE_TYPE, canvasState, currentAngleTypeSelector, pitchTextSelector } from '@/store/canvasAtom'
 import { useRecoilValue } from 'recoil'
 import { fabric } from 'fabric'
-import { findAndRemoveClosestPoint, getDegreeByChon, getDegreeInOrientation, isPointOnLine } from '@/util/canvas-util'
+import { calculateIntersection, findAndRemoveClosestPoint, getDegreeByChon, getDegreeInOrientation, isPointOnLine } from '@/util/canvas-util'
 import { QPolygon } from '@/components/fabric/QPolygon'
 import { isSamePoint, removeDuplicatePolygons } from '@/util/qpolygon-utils'
 import { flowDisplaySelector } from '@/store/settingAtom'
@@ -1034,6 +1034,130 @@ export const usePolygon = () => {
 
     let allLines = [...polygonLines, ...innerLines]
 
+    // allLines를 전부 돌면서 교차점이 있는 경우 그 line을 잘라서 allLines에 추가
+    const processIntersections = () => {
+      const linesToProcess = canvas.getObjects().filter((obj) => obj.type === 'QLine' && obj.name === 'auxiliaryLine' && obj.visible)
+      const newDividedLines = []
+      const processedLines = new Set()
+
+      for (let i = 0; i < linesToProcess.length; i++) {
+        for (let j = i + 1; j < linesToProcess.length; j++) {
+          const line1 = linesToProcess[i]
+          const line2 = linesToProcess[j]
+
+          // 이미 처리된 line들은 건너뛰기
+          if (processedLines.has(line1) || processedLines.has(line2)) continue
+
+          // 같은 line이거나 이미 연결된 line은 건너뛰기
+          if (line1 === line2) continue
+          if (
+            isSamePoint({ x: line1.x1, y: line1.y1 }, { x: line2.x1, y: line2.y1 }) ||
+            isSamePoint({ x: line1.x1, y: line1.y1 }, { x: line2.x2, y: line2.y2 }) ||
+            isSamePoint({ x: line1.x2, y: line1.y2 }, { x: line2.x1, y: line2.y1 }) ||
+            isSamePoint({ x: line1.x2, y: line1.y2 }, { x: line2.x2, y: line2.y2 })
+          ) {
+            continue
+          }
+
+          const intersectionPoint = calculateIntersection(line1, line2)
+          if (intersectionPoint) {
+            // line1에 교차점 추가
+            if (!line1.intersectionPoints) line1.intersectionPoints = []
+            line1.intersectionPoints.push(intersectionPoint)
+
+            // line2에 교차점 추가
+            if (!line2.intersectionPoints) line2.intersectionPoints = []
+            line2.intersectionPoints.push(intersectionPoint)
+          }
+        }
+      }
+
+      // 교차점이 있는 line들을 분할
+      linesToProcess.forEach((line) => {
+        if (line.intersectionPoints && line.intersectionPoints.length > 0) {
+          // 교차점들을 line의 시작점에서부터의 거리순으로 정렬
+          const sortedPoints = line.intersectionPoints.sort((a, b) => {
+            const distA = Math.hypot(a.x - line.x1, a.y - line.y1)
+            const distB = Math.hypot(b.x - line.x1, b.y - line.y1)
+            return distA - distB
+          })
+
+          let currentPoint = { x: line.x1, y: line.y1 }
+
+          // 각 교차점까지의 line segment 생성
+          sortedPoints.forEach((intersectionPoint) => {
+            if (!isSamePoint(currentPoint, intersectionPoint)) {
+              const newLine = new QLine([currentPoint.x, currentPoint.y, intersectionPoint.x, intersectionPoint.y], {
+                stroke: line.stroke,
+                strokeWidth: line.strokeWidth,
+                fontSize: line.fontSize,
+                attributes: { ...line.attributes },
+                name: line.name,
+                visible: line.visible,
+              })
+              // startPoint와 endPoint 설정
+              if (newLine.x1 < newLine.x2) {
+                newLine.startPoint = { x: newLine.x1, y: newLine.y1 }
+                newLine.endPoint = { x: newLine.x2, y: newLine.y2 }
+              } else if (newLine.x1 > newLine.x2) {
+                newLine.startPoint = { x: newLine.x2, y: newLine.y2 }
+                newLine.endPoint = { x: newLine.x1, y: newLine.y1 }
+              } else {
+                if (newLine.y1 < newLine.y2) {
+                  newLine.startPoint = { x: newLine.x1, y: newLine.y1 }
+                  newLine.endPoint = { x: newLine.x2, y: newLine.y2 }
+                } else {
+                  newLine.startPoint = { x: newLine.x2, y: newLine.y2 }
+                  newLine.endPoint = { x: newLine.x1, y: newLine.y1 }
+                }
+              }
+              newDividedLines.push(newLine)
+            }
+            currentPoint = intersectionPoint
+          })
+
+          // 마지막 교차점에서 line 끝점까지의 segment
+          const endPoint = { x: line.x2, y: line.y2 }
+          if (!isSamePoint(currentPoint, endPoint)) {
+            const newLine = new QLine([currentPoint.x, currentPoint.y, endPoint.x, endPoint.y], {
+              stroke: line.stroke,
+              strokeWidth: line.strokeWidth,
+              fontSize: line.fontSize,
+              attributes: { ...line.attributes },
+              name: line.name,
+              visible: line.visible,
+            })
+            // startPoint와 endPoint 설정
+            if (newLine.x1 < newLine.x2) {
+              newLine.startPoint = { x: newLine.x1, y: newLine.y1 }
+              newLine.endPoint = { x: newLine.x2, y: newLine.y2 }
+            } else if (newLine.x1 > newLine.x2) {
+              newLine.startPoint = { x: newLine.x2, y: newLine.y2 }
+              newLine.endPoint = { x: newLine.x1, y: newLine.y1 }
+            } else {
+              if (newLine.y1 < newLine.y2) {
+                newLine.startPoint = { x: newLine.x1, y: newLine.y1 }
+                newLine.endPoint = { x: newLine.x2, y: newLine.y2 }
+              } else {
+                newLine.startPoint = { x: newLine.x2, y: newLine.y2 }
+                newLine.endPoint = { x: newLine.x1, y: newLine.y1 }
+              }
+            }
+            newDividedLines.push(newLine)
+          }
+
+          processedLines.add(line)
+        }
+      })
+
+      // allLines 업데이트: 분할된 line들 제거하고 새 line들 추가
+      allLines = allLines.filter((line) => !processedLines.has(line))
+      allLines = [...allLines, ...newDividedLines]
+    }
+
+    // 교차점 처리 실행
+    processIntersections()
+
     /*allLines.forEach((line) => {
       const originColor = line.stroke